Integration

This is a good time to see how the new biological model and gear types interact with the old modules seamlessly.

We now have a biology module that represents fish by number splitting them in age and sex cohorts. We now also have gear that can target some cohorts more or less than others.
Here I take Dover Sole, deplete it (leaving only 1% alive) and distribute it over the conceptual map. If we let 200 (conceptual) fishers loose on this map we generate again that kind of expanding fishing front we are used to by now:

This is nice as it implies that this dynamic is robust to changes in the biology module.

Here I am using the new recruitment formulas Steve Saul coded from the stock assessment. I show the evolution of biomass over 4 scenarios: one where there is no fisher, 50 fishers, 100 or 200. This is to show that the dover sole population in this scenario has the potential to boom but not when there are too many boats targeting it.

Selectivity

Rather than changing the number of fishers, let’s just say that our only policy lever is gear regulation. To make it simple imagine that catchability is fixed at \(q=0.01\) but we can change the selectivity of the gear. To make things even simpler imagine that the shape of the selectivity is the indicator function: selectivity is 0 for all fish whose length is below \(x\) and 1 for all the others.
We are interested in the \(x\) that maximizes long term (20 years) catches.
This is a straightforward 1-dimensional maximization and we can use the Bayesian optimizer. What follows is the posterior:

The posterior is maximised around 25.75 cm which is a length soles reaches and pass when they are 6 years old. Keeping fish younger than 6 alive seems to strike the right balance between managing the stock and exploiting it.
This means that even with 200 fishers the biomass grows fast enough to never deplete: